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Article Dans Une Revue Annales Henri Poincaré Année : 2002

Remarks on nonlinear Schrödinger equations with harmonic potential

Résumé

Bose-Einstein condensation is usually modeled by nonlinear Schrödinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the blow up time.

Dates et versions

hal-00004963 , version 1 (24-05-2005)

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Citer

Rémi Carles. Remarks on nonlinear Schrödinger equations with harmonic potential. Annales Henri Poincaré, 2002, 3, pp.757-772. ⟨10.1007/S00023-002-8635-4⟩. ⟨hal-00004963⟩

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